Uncertainty theory is a branch of mathematics for modeling uncertainty in human reasoning, and uncertain statistics is a methodology for collecting and interpreting experts’ experimental data by uncertainty theory. In this paper, we will first discuss how to collect experts’ data. We apply this method to a model for estimating the distance between Beijing and Tianjin. Based on the experts’ expe...

To properly interpret the quality of a gamma-spectroscopy measurement, an uncertainty estimate must be made. The uncertainty in the efficiency calibration is the dominant component to the total propagated measurement uncertainty for many types of measurements. Any deviations between the as-calibrated geometry and the as-measured geometry contribute to the total uncertainty. A mathematical techn...

We show how the Model-Free Prediction Principle of Politis (2013) can be applied to nonparametric regression with a univariate response and regressors that are high-dimensional or even infinite-dimensional, i.e., functional. Without assuming an additive model with i.i.d. errors, the Model-Free Principle is capable of yielding both consistent predictors as well as prediction intervals. 39.

In times of globalization, differences between cultures and in the interpretation of linguistic terms can lead to misunderstanding in communication. The present study focuses on the influence of cultural dimensions, especially uncertainty avoidance, on the interpretation of verbal probability expressions. It is hypothesized that uncertainty avoidance has an effect on the interpretation of uncer...

This paper is devoted to obtaining an averaging principle for systems of slow-fast stochastic differential equations, where the fast variable drift is periodically modulated on a fast time-scale. The approach developed here combines probabilistic methods with a recent analytical result on long-time behavior for second order elliptic equations with time-periodic coefficients.

The current study investigated how young learners’ experiences with arithmetic equations can lead to learning of an arithmetic principle. The focus was elementary school children’s acquisition of the Relation to Operands principle for subtraction (i.e., for natural numbers, the difference must be less than the minuend). In Experiment 1, children who viewed incorrect, principle-consistent equati...

Infinite product formulae for conformally mapping an unbounded multiply connected circle domain to an unbounded canonical radial or circular slit domain, or to domains with both radial and circular slit boundary components are derived and implemented numerically and graphically. The formulae are generated by analytic continuation with the reflection principle. Convergence of the infinite produc...

Structural analysis and design has to be performed by considering uncertainties both in loading and structural properties respectively. While in traditional analysis and design procedures these uncertainties were take into acount in a qualitative manner in order to adhere to deterministic concepts modern procedures are shown to allow their quantitative processing. This way a rational treatment ...

In the field of uncertainty quantification, uncertainty in the governing equations may assume two forms: aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty can be characterised by known probability distributions whilst epistemic uncertainty arises from a lack of knowledge of probabilistic information. While extensive research efforts have been devoted to the numerical treatmen...

One of the biggest challenges in speaker recognition is incomplete observations in test phase caused by availability of only short duration utterances. The problem with short utterances is that speaker recognition needs to be handled by having information from only limited amount of acoustic classes. By considering limited observations from a test speaker, the resulting i-vector as a representa...